Oscillation Analysis For Two Kinds Of Nonlinear Delay Differential Equations

This paper mainly analyzes oscillation of two kinds of nonlinear delay differential equations,one of which is a kind of nonlinear neutral delay differential equation and the other is a kind of nonlinear chronic myelogenous leukemia model.Nowadays,there are many researh articles on stability of delay differential equations,but there are still relatively few research articles on oscillation of numerical solution, and it is limited to several types of relatively simple and special delay differential equations,and most of them are about linear models.So research articles on oscillation of nonlinear models are rare.It has a very wide application for nonlinear models in all aspects of life.By studying these two kinds of nonlinear delay differential equations,can help us analyze actual situation in a more detailed way,so the research of this topic is of great significance.In the first chapter,the background of delay differential equations is given in detail7and some developments relate to the oscillation aspects of the numerical solutions of delay differential equations are summarized.In the second chapter of this paper,some theorems and definitions of differential equations are given.There are also three commonly used inequalities.In the third chapter,we study oscillation of analytical solution for a class of nonlinear constant coefficient neutral delay equations with multiple delays.For this neutral model,we obtain the sufficient conditions of oscillation of analytical solution for the model when 0<p<1,and when p?1 necessary and sufficient conditions of oscillation of analytical solution for the model.And the corresponding examples are given.For the nonlinear chronic myeloid leukemia model,the sufficient conditions for oscillation of analytical solutions and numerical solutions of the equation are obtained.Finally,asymptotic behavior of non-oscillation solution is proved.In the fourth chapter,some theoretical results on oscillation and non-oscillation of analytical and numerical solutions for a type of nonlinear chronic myelogenous leukemia models axe analyzed.For this model,we use the linearization condition.By analyzing roots of characteristic equation,sufficient condition of oscillation of analytic solutions for this equation is obtained.For this differential equation mod-el,by using the linear ?-method,It is transformed into a delay difference equation.Finally,sufficient condition of oscillation of numerical solutions is obtained by us-ing oscillation theorem of difference equation.Under the condition of guaranteeing oscillation of analytical solutions,linear ?-method maintains sufficient condition for oscillation of numerical solutions,and asymptotic nature of non-oscillation numer-ical solutions are obtained.In order to validate our theory,some corresponding examples to reflect the correctness of results that we get will be given.